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Monte Carlo Studies of Quantum Critical Metals
- Erez Berg1, Samuel Lederer2, Yoni Schattner3,4, and Simon Trebst5
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View Affiliations Hide AffiliationsAffiliations: 1Department of Physics, James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA; email: [email protected] 2Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 3Department of Physics, Stanford University, Stanford, California 94305, USA 4Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA 5Institute for Theoretical Physics, University of Cologne, Cologne 50937, Germany
- Vol. 10:63-84 (Volume publication date March 2019) https://doi.org/10.1146/annurev-conmatphys-031218-013339
- First published as a Review in Advance on November 16, 2018
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Copyright © 2019 by Annual Reviews. All rights reserved
Abstract
Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high-temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this review, we examine the status of the understanding of metallic quantum criticality and the recent progress made by QMC simulations. We focus on the cases of spin-density wave and Ising nematic criticality. We describe the results obtained so far and their implications for superconductivity, non-Fermi liquid behavior, and transport near metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.
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